
# 1) The first transformation is a horizontal expansion. You can see that b doesn't
#     change length, while a grows longer. Since these eigenvectors are aligned
#     with the axes, we know that there is no movement in the vertical direction
#     (based on b) and an expansion in the horizontal direction (based on a).

#. 2) This transformation is a reflection over the line y = x. Neither eigenvector
#    changes length, a is along the line y = x and b is flipped over it.